Predictions of the fusion-by-diffusion model for the synthesis cross sections of $Z=114$--120 elements based on macroscopic-microscopic fission barriers

Predictions of the fusion-by-diffusion model for the synthesis cross sections of $Z = 114$ –120 elements based on macroscopic-microscopic fission barriers

K. Siwek-Wilczyńska, T. Cap, M. Kowal, A. Sobiczewski, and J. Wilczyński

Phys. Rev. C 86, 014611 – Published 16 July 2012

Abstract

A complete set of existing data on hot fusion reactions leading to synthesis of superheavy nuclei of $Z = 114 - 118$ , obtained in a series of experiments in Dubna and later in GSI Darmstadt and LBNL Berkeley, was analyzed in terms of an angular-momentum-dependent version of the fusion-by-diffusion (FBD) model with fission barriers and ground-state masses taken from the Warsaw macroscopic-microscopic model (involving nonaxial shapes) of Kowal et al. The only empirically adjustable parameter of the model, the injection-point distance ( $s_{inj}$ ), has been determined individually for all the reactions. Very regular systematics of this parameter have been established. The regularity of the obtained $s_{inj}$ systematics indirectly points at the internal consistency of the whole set of fission barriers used in the calculations. (In an attempt to fit the same set of data by using the alternative theoretical fission barriers of Möller et al. we did not obtain such a consistent result.) Having fitted all the experimental excitation functions for elements $Z = 114$ –118, the FBD model was used to predict cross sections for synthesis of elements $Z = 119$ and 120. Regarding prospects to produce the new element $Z = 119$ , our calculations prefer the $^{252}$ Es( $^{48}$ Ca,xn) $^{300 - x}$ 119 reaction, for which the synthesis cross section of about 0.2 pb in $4 n$ channel at $E_{c . m .} \approx 220$ MeV is expected. The most favorable reaction to synthesize the element $Z$ $=$ 120 turns out to be $^{249}$ Cf( $^{50}$ Ti,xn) $^{299 - x}$ 120, but the predicted cross section for this reaction is only 6 fb (for $3 n$ and $4 n$ channels).

Received 20 November 2011

DOI:https://doi.org/10.1103/PhysRevC.86.014611

Authors & Affiliations

K. Siwek-Wilczyńska¹, T. Cap¹, M. Kowal², A. Sobiczewski², and J. Wilczyński³

¹Institute of Experimental Physics, Faculty of Physics, University of Warsaw, Hoża 69, 00-681 Warsaw, Poland
²National Centre for Nuclear Research, Hoża 69, 00-681 Warsaw, Poland
³National Centre for Nuclear Research, 05-400 Otwock-Świerk, Poland

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Vol. 86, Iss. 1 — July 2012

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Images

Figure 1
Systematics of the injection-point distance $s_{inj}$ as a function of the kinetic energy excess $E_{c . m .} - B_{0}$ above the Coulomb barrier $B_{0}$ . Values of $s_{inj}$ have been determined for each reaction and each particular $x n$ channel by fitting the theoretical cross section at the maximum of a given $x n$ excitation function to the data. The calculations have been done for the fission-barrier heights and ground-state masses of Kowal et al. [21, 22]. Complete list of the analyzed reactions with references is given in the text. Identical symbols for a given $Z$ and a given experiment refer to data for consecutive $x n$ channels.Reuse & Permissions
Figure 2
Energy dependence of the cross section for synthesis of superheavy nuclei in hot fusion reactions. Full circles represent data for $3 n$ , $4 n,$ and $5 n$ reaction channels obtained in Dubna experiments for elements $Z$ $=$ 114–118 [3, 24, 25, 26, 27, 29, 34]; open circles represent data obtained at GSI Darmstadt for $Z$ $=$ 114 and 116 [30, 32]. Data are compared with excitation functions for separate $x n$ channels, calculated with the FBD model assuming fission barriers and ground-state masses of Kowal et al. [21, 22] and the systematics of the injection-point distance [Eq. (3)].Reuse & Permissions
Figure 3
Dependence of the injection-point distance $s_{inj}$ on the kinetic energy excess $E_{c . m .} - B_{0}$ above the Coulomb barrier $B_{0}$ , deduced from analysis of experimental data [3, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34] the same way as in Fig. 1, but assuming the fission-barrier heights [20] and ground-state masses [18] of Möller et al. (see text).Reuse & Permissions
Figure 4
Excitation functions for the $3 n$ and $4 n$ channels of the $^{243}$ Am( $^{48}$ Ca, $x n$ ) $^{291 - x}$ 115 reaction calculated with the FBD model assuming the fission barriers [20] and ground-state masses [18] of Möller et al. (dashed lines) compared with the experimental cross sections [3, 24, 34] and the predictions for the fission barriers and ground-state masses of Kowal et al. [21, 22] (solid lines). In the absence of clear correlation between $s_{inj}$ and $E_{c . m .} - B_{0}$ for the barriers of Möller et al. (see Fig. 3), the dashed lines were calculated for a fixed value $s_{inj}$ $=$ 7.2 fm (the mean value).Reuse & Permissions
Figure 5
Synthesis cross sections of yet undiscovered superheavy nuclei of $Z$ $=$ 119 and 120 predicted by using the fusion-by-diffusion (FBD) model with fission barriers and ground-state masses of Kowal et al. [21, 22] and the systematics of the injection-point distance [Eq. (3)] (see text).Reuse & Permissions

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